Tools

"... The Gibbs sampler can be used to obtain samples of arbitrary size from the posterior distribution over the parameters of a structural equation model (SEM) given covariance data and a prior distribution over the parameters. Point estimates, standard deviations and interval estimates for the parameter ..."

The Gibbs sampler can be used to obtain samples of arbitrary size from the posterior distribution over the parameters of a structural equation model (SEM) given covariance data and a prior distribution over the parameters. Point estimates, standard deviations and interval estimates for the parameters can be computed from these samples. If the prior distribution over the parameters is uninformative, the posterior is proportional to the likelihood, and asymptotically the inferences based on the Gibbs sample are the same as those based on the maximum likelihood solution, e.g., output from LISREL or EQS. In small samples, however, the likelihood surface is not Gaussian and in some cases contains local maxima. Nevertheless, the Gibbs sample comes from the correct posterior distribution over the parameters regardless of the sample size and the shape of the likelihood surface. With an informative prior distribution over the parameters, the posterior can be used to make inferences about the parameters of underidentified models, as we illustrate on a simple errors-in-variables model.

"... The most widely used multivariate statistical models in the social and behavioral sciences involve linear structural relations among observed and latent variables. In practice, these variables are generally nonnormally distributed, and hence classical multivariate analysis, based on multinormal erro ..."

The most widely used multivariate statistical models in the social and behavioral sciences involve linear structural relations among observed and latent variables. In practice, these variables are generally nonnormally distributed, and hence classical multivariate analysis, based on multinormal error-free variables having no simultaneous interrelations, is not adequate to deal with such data. Since structural relations among variables imply a structure for the multivariate product moments of the variables, general methods for the analysis of mean and covariance structures have been proposed to estimate and test particular model structures. Unfortunately, extant statistical tests, such as the likelihood ratio test (LRT) and a test based on asymptotically distribution free (ADF) covariance structure analysis, have been found to be virtually useless in practical model evaluation at finite sample sizes with nonnormal data. For example, in one condition of a simulation on confirmatory facto...

"... Research and Evaluation Methodology Program, and for supporting me to finish my doctoral study. I owe much gratitude to the faculty of Department of Educational Psychology for his/her excellent lecture and thoughtful consideration. The completion of this dissertation would not be possible without th ..."

Research and Evaluation Methodology Program, and for supporting me to finish my doctoral study. I owe much gratitude to the faculty of Department of Educational Psychology for his/her excellent lecture and thoughtful consideration. The completion of this dissertation would not be possible without the guidance of my dissertation committee. Each has helped me throughout my dissertation in his/her own ways. I especially wish to thank Dr. James Algina, my supervisory committee chair and advisor, for his precious time, professional mentoring, and valuable guidance during the last four years. I also wish to thank Dr. David Miller for his consideration and useful advice which made my

"... Abstract. This paper presents a theoretical development that extends results on the distribution of the sample correlation coefficient and the Fisher transform (Fisher, 1921). Several well known correlational procedures use the Fisher transform or its square as the basis of hypothesis testing. These ..."

Abstract. This paper presents a theoretical development that extends results on the distribution of the sample correlation coefficient and the Fisher transform (Fisher, 1921). Several well known correlational procedures use the Fisher transform or its square as the basis of hypothesis testing. These procedures assume that the variance of the Fisher transform can be approximated adequately as 1/ ( n − 3). We present results that demonstrate that for small sample size this is not necessarily true. We present results that demonstrate that for small sample size this is not necessarily true. Exact moments of the Fisher transform and its square are computed for both null and non-null correlations for small n ( ≤ 20). An extension of the classic series expansion formulae of Hotelling (Hotelling, 1953) for the moments of the Fisher transform and its square are discussed and compared with the exact moments of the Fisher transform and its square. Monte Carlo experiments are used to demonstrate how these results may produce significant improvements in the small sample performance of tests for pattern hypothesis on correlation matrices. 1.

This thesis tests Oliver Williamson’s proposition that transaction cost economics can explain the limits of firm size. Williamson suggests that diseconomies of scale are manifested through four interrelated factors: atmospheric consequences due to specialisation, bureaucratic insularity, incentive limits of the employment relation and communication distortion due to bounded rationality. Furthermore, Williamson argues that diseconomies of scale are counteracted by economies of scale and can be moderated by adoption of the multidivisional organisation form and by high internal asset specificity. Combined, these influences tend to cancel out and thus there is not a strong, directly observable, relationship between a large firm’s size and performance. A review of the relevant literature, including transaction cost economics, sociological studies of bureaucracy, information-processing perspectives on the firm, agency theory, and studies of incentives and motivation

"... Covariance structure analysis is often used for inference and for dimension reduction with high dimensional data. When data is not normally distributed, the asymptotic distribution free (ADF) method is often used to fit a proposed model. This approach uses a weight matrix based on the inverse of the ..."

Covariance structure analysis is often used for inference and for dimension reduction with high dimensional data. When data is not normally distributed, the asymptotic distribution free (ADF) method is often used to fit a proposed model. This approach uses a weight matrix based on the inverse of the matrix formed by the sample fourth moments and sample covariances. The ADF test statistic is asymptotically distributed as a chi-square variate, but its empirical performance rejects the true model too often at all but impractically large sample sizes. By comparing mean and covariance structure analysis with its peer in the multivariate linear model, we propose some modified ADF test statistics as F-tests whose distributions we approximate using F-distributions. Empirical studies show that the distributions of the new F-tests are more closely approximated by F-distributions than are the original ADF statistics when referred to chi-square distributions. Detailed analysis indicates why the AD...